Taylor-plasticity-based analysis of length scale effects in void growth

Handle URI:
http://hdl.handle.net/10754/563764
Title:
Taylor-plasticity-based analysis of length scale effects in void growth
Authors:
Liu, Junxian; Demiral, Murat; El Sayed, Tamer S.
Abstract:
We have studied the void growth problem by employing the Taylor-based strain gradient plasticity theories, from which we have chosen the following three, namely, the mechanism-based strain gradient (MSG) plasticity (Gao et al 1999 J. Mech. Phys. Solids 47 1239, Huang et al 2000 J. Mech. Phys. Solids 48 99-128), the Taylor-based nonlocal theory (TNT; 2001 Gao and Huang 2001 Int. J. Solids Struct. 38 2615) and the conventional theory of MSG (CMSG; Huang et al 2004 Int. J. Plast. 20 753). We have addressed the following three issues which occur when plastic deformation at the void surface is unconstrained. (1) Effects of elastic deformation. Elasticity is essential for cavitation instability. It is therefore important to guarantee that the gradient term entering the Taylor model is the effective plastic strain gradient instead of the total strain gradient. We propose a simple elastic-plastic decomposition method. When the void size approaches the minimum allowable initial void size related to the maximum allowable geometrically necessary dislocation density, overestimation of the flow stress due to the negligence of the elastic strain gradient is on the order of lεY/R0 near the void surface, where l, εY and R0 are, respectively, the intrinsic material length scale, the yield strain and the initial void radius. (2) MSG intrinsic inconsistency, which was initially mentioned in Gao et al (1999 J. Mech. Phys. Solids 47 1239) but has not been the topic of follow-up studies. We realize that MSG higher-order stress arises due to the linear-strain-field approximation within the mesoscale cell with a nonzero size, lε. Simple analysis shows that within an MSG mesoscale cell near the void surface, the difference between microscale and mesoscale strains is on the order of (lε/R0)2, indicating that when lε/R0 ∼ 1.0, the higher-order stress effect can make the MSG result considerably different from the TNT or CMSG results. (3) Critical condition for cavitation instability. When Taylor plasticity replaces classical plasticity as the flow rule, the critical cavitation condition, appearing when the derivative of the externally imposed mean stress with respect to the current void radius becomes zero, is rewritten analytically according to the Leibniz relation and found to be very different from the classical counterpart.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Publisher:
IOP Publishing
Journal:
Modelling and Simulation in Materials Science and Engineering
Issue Date:
25-Sep-2014
DOI:
10.1088/0965-0393/22/7/075005
Type:
Article
ISSN:
09650393
Sponsors:
The work of J X Liu was supported by the Jiangsu University and Jiangsu Specially-Appointed Professor grants, Jiangsu Science Fund for Youth with the number BK20140520 and Jiangsu "Shuang-Chang" funding. This work was also partially funded by the KAUST baseline fund. We give special thanks to Professor Yonggang Huang and Professor Huajian Gao for their valuable discussions and suggestions.
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Junxianen
dc.contributor.authorDemiral, Muraten
dc.contributor.authorEl Sayed, Tamer S.en
dc.date.accessioned2015-08-03T12:09:21Zen
dc.date.available2015-08-03T12:09:21Zen
dc.date.issued2014-09-25en
dc.identifier.issn09650393en
dc.identifier.doi10.1088/0965-0393/22/7/075005en
dc.identifier.urihttp://hdl.handle.net/10754/563764en
dc.description.abstractWe have studied the void growth problem by employing the Taylor-based strain gradient plasticity theories, from which we have chosen the following three, namely, the mechanism-based strain gradient (MSG) plasticity (Gao et al 1999 J. Mech. Phys. Solids 47 1239, Huang et al 2000 J. Mech. Phys. Solids 48 99-128), the Taylor-based nonlocal theory (TNT; 2001 Gao and Huang 2001 Int. J. Solids Struct. 38 2615) and the conventional theory of MSG (CMSG; Huang et al 2004 Int. J. Plast. 20 753). We have addressed the following three issues which occur when plastic deformation at the void surface is unconstrained. (1) Effects of elastic deformation. Elasticity is essential for cavitation instability. It is therefore important to guarantee that the gradient term entering the Taylor model is the effective plastic strain gradient instead of the total strain gradient. We propose a simple elastic-plastic decomposition method. When the void size approaches the minimum allowable initial void size related to the maximum allowable geometrically necessary dislocation density, overestimation of the flow stress due to the negligence of the elastic strain gradient is on the order of lεY/R0 near the void surface, where l, εY and R0 are, respectively, the intrinsic material length scale, the yield strain and the initial void radius. (2) MSG intrinsic inconsistency, which was initially mentioned in Gao et al (1999 J. Mech. Phys. Solids 47 1239) but has not been the topic of follow-up studies. We realize that MSG higher-order stress arises due to the linear-strain-field approximation within the mesoscale cell with a nonzero size, lε. Simple analysis shows that within an MSG mesoscale cell near the void surface, the difference between microscale and mesoscale strains is on the order of (lε/R0)2, indicating that when lε/R0 ∼ 1.0, the higher-order stress effect can make the MSG result considerably different from the TNT or CMSG results. (3) Critical condition for cavitation instability. When Taylor plasticity replaces classical plasticity as the flow rule, the critical cavitation condition, appearing when the derivative of the externally imposed mean stress with respect to the current void radius becomes zero, is rewritten analytically according to the Leibniz relation and found to be very different from the classical counterpart.en
dc.description.sponsorshipThe work of J X Liu was supported by the Jiangsu University and Jiangsu Specially-Appointed Professor grants, Jiangsu Science Fund for Youth with the number BK20140520 and Jiangsu "Shuang-Chang" funding. This work was also partially funded by the KAUST baseline fund. We give special thanks to Professor Yonggang Huang and Professor Huajian Gao for their valuable discussions and suggestions.en
dc.publisherIOP Publishingen
dc.subjectcavitation instabilityen
dc.subjectGNDen
dc.subjecthigher-order stressen
dc.subjectlength-scale effecten
dc.subjectstrain gradient decompositionen
dc.subjectTaylor dislocation relationen
dc.subjectvoid growthen
dc.titleTaylor-plasticity-based analysis of length scale effects in void growthen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalModelling and Simulation in Materials Science and Engineeringen
dc.contributor.institutionFaculty of Civil Engineering and Mechanics, Jiangsu University, Xuefu Road 301Zhenjiang, Jiangsu Province, Chinaen
dc.contributor.institutionDepartment of Mechanical Engineering, University of Turkish Aeronautical AssociationAnkara, Turkeyen
kaust.authorDemiral, Muraten
kaust.authorEl Sayed, Tamer S.en
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